Mathematics - Permutation & Combination Question with Solution | TestHub

There are 5 points $P_1,P_2,P_3,P_4,P_5$ on the side $AB$, excluding $A$ and $B$, of a triangle $ABC$. Similarly there are 6 points ${\mathrm{P}}_6,{\mathrm{P}}_7,\dots ,{\mathrm{P}}_{11}$ on the side $\mathrm{BC}$ and 7 points ${\mathrm{P}}_{12},{\mathrm{P}}_{13},\dots ,{\mathrm{P}}_{18}$ on the side $CA$ of the triangle. The number of triangles, that can be formed using the points ${\mathrm{P}}_1,{\mathrm{P}}_2,\dots ,{\mathrm{P}}_{18}$ as vertices, is :